हिंदी

Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choose the correct answer.

Advertisements
Advertisements

प्रश्न

Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choose the correct answer.

विकल्प

  • (2, 4) ∈ R

  • (3, 8) ∈ R

  • (6, 8) ∈ R

  • (8, 7) ∈ R

MCQ
Advertisements

उत्तर

(6, 8) ∈ R

Explanation:

R = {(a, b) : a = b – 2, b > 6}

Here, since b > 6, hence (2, 4) ∉ R and

3 ≠ 8 – 2, ∴ (3, 8) ∉ R and

8 ≠ 7 – 2, ∴ (8, 7) ∉ R

Now for (6, 8), 8 > 6 and 6 = 8 – 2

∴ (6, 8) ∈ R ≠ R

Hence, option (6, 8) ∈ R is correct.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations and Functions - EXERCISE 1.1 [पृष्ठ ७]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 1 Relations and Functions
EXERCISE 1.1 | Q 16. | पृष्ठ ७

संबंधित प्रश्न

If R=[(x, y) : x+2y=8] is a relation on N, write the range of R.


Show that the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12} given by R = {(a, b) : a = b} is an equivalence relation. Find the set of all elements related to 1.


Given an example of a relation. Which is transitive but neither reflexive nor symmetric.


Given an example of a relation. Which is reflexive and transitive but not symmetric.


Given a non-empty set X, consider P(X), which is the set of all subsets of X. Define the relation R in P(X) as follows:

For subsets A, B in P(X), ARB if and only if A ⊂ B. Is R an equivalence relation on P(X)? Justify your answer.


Let A = {1, 2, 3}, and let R1 = {(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)}, R2 = {(2, 2), (3, 1), (1, 3)}, R3 = {(1, 3), (3, 3)}. Find whether or not each of the relations R1, R2, R3 on A is (i) reflexive (ii) symmetric (iii) transitive.


The following relation is defined on the set of real numbers.
aRb if a – b > 0

Find whether relation is reflexive, symmetric or transitive.


Give an example of a relation which is symmetric and transitive but not reflexive?


Give an example of a relation which is transitive but neither reflexive nor symmetric?


Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, add a minimum number of ordered pairs so that the enlarged relation is symmeteric, transitive and reflexive.


Defines a relation on N:

xy is square of an integer, x, y ∈ N

Determine the above relation is reflexive, symmetric and transitive.


m is said to be related to n if m and n are integers and m − n is divisible by 13. Does this define an equivalence relation?


Let R be the relation defined on the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}.


Let A = {2, 3, 4, 5} and B = {1, 3, 4}. If R is the relation from A to B given by a R b if "a is a divisor of b". Write R as a set of ordered pairs.


If a relation R is defined on the set Z of integers as follows:
(a, b) ∈ R ⇔ a2 + b2 = 25. Then, domain (R) is ___________


A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by : x R y ⇔ x is relatively prime to y. Then, domain of R is ______________ .


 If A = {a, b, c, d}, then a relation R = {(a, b), (b, a), (a, a)} on A is _____________ .


In the set Z of all integers, which of the following relation R is not an equivalence relation ?


Mark the correct alternative in the following question:

Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if l is perpendicular to m for all l, m  L. Then, R is ______________ .


Mark the correct alternative in the following question:

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b for all a, b  T. Then, R is ____________ .


If `f(x) = (4x + 3)/(6x - 4), x ≠ 2/3`, show that fof (x) = x for all `x ≠ 2/3`. Also, find the inverse of f.


Show that the relation R defined by (a, b)R(c,d) ⇒ a + d = b + c   on the A x A  , where A =  {1, 2,3,...,10}  is an equivalence relation. Hence write the equivalence class [(3, 4)]; a, b, c,d ∈ A.


Write the relation in the Roster form and hence find its domain and range :
R1 = {(a, a2) / a is prime number less than 15}


For real numbers x and y, define xRy if and only if x – y + `sqrt(2)` is an irrational number. Then the relation R is ______.


Let R be relation defined on the set of natural number N as follows:
R = {(x, y): x ∈N, y ∈N, 2x + y = 41}. Find the domain and range of the relation R. Also verify whether R is reflexive, symmetric and transitive


Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
a mapping from A to B which is not injective


Give an example of a map which is neither one-one nor onto


The maximum number of equivalence relations on the set A = {1, 2, 3} are ______.


If A is a finite set containing n distinct elements, then the number of relations on A is equal to ____________.


Let `"f"("x") = ("x" - 1)/("x" + 1),` then f(f(x)) is ____________.


Let A = {1, 2, 3, …. n} and B = {a, b}. Then the number of surjections from A into B is ____________.


Total number of equivalence relations defined in the set S = {a, b, c} is ____________.


Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.

A = {S, D}, B = {1,2,3,4,5,6}

  • Let R: B → B be defined by R = {(1,1),(1,2), (2,2), (3,3), (4,4), (5,5), (6,6)}, then R is ____________.

If A is a finite set consisting of n elements, then the number of reflexive relations on A is


The relation > (greater than) on the set of real numbers is


Let a set A = A1 ∪ A2 ∪ ... ∪ Ak, where Ai ∩ Aj = Φ for i ≠ j, 1 ≤ i, j ≤ k. Define the relation R from A to A by R = {(x, y): y ∈ Ai if and only if x ∈ Ai, 1 ≤ i ≤ k}. Then, R is ______.


If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×